Perm Dynamo Days
Workshop
7-11 February 2005
Abstracts
Edited by Peter Frick
Perm, Russia
ORGANIZED BY:
Institute of Continuous Media Mechanics UB RAS
SUPPORTED BY:
InternationalScience & TechnologyCenter
Dynasty Foundation
Russian Foundation for Basic Research
Ural Branch of the RussianAcademy of Sciences
SCIENTIFIC COMMITTEE:
A. Brandenburg (Copenhagen, Denmark)
B. Dubrulle (Saclay, France)
C. Forest (Madison, USA)
P. Frick (Perm, Russia) – Chairman
A. Gailitis (Riga, Latvia)
G. Gerbeth (Rossendorf, Germany)
V. Matveenko (Perm, Russia)
M.R.E. Proctor (Cambridge, UK)
D. Sokoloff (Moscow, Russia)
A. Shukurov (Newcastle, UK)
LOCAL COMMITTEE:
P. Frick
G. Levina
R. Stepanov
G. Tsaplina
Prepared for printing: I. Burylov, G. Levina, R. Stepanov
Dynamo theory and its experimental validation:earlier attempts and perspectives
K.-H. Rädler
Astrophysical Institute Potsdam,Potsdam,Germany
It is generally believed that the magnetic fields of the Earth and the Sun, of some planets and many types of stars as well as those of galaxies are due to dynamo action of motions in the electrically conducting interiors of these objects. The dynamo proved to be one of the basic phenomena in the cosmos. Since the sixties of the last century dynamo theory has been widely elaborated. In the last decade much progress has been made in direct numerical simulations of dynamo processes in specific objects.
This development was accompanied by activities to design and perform laboratory experiments on dynamo action in electrically conducting fluids. Only in 1999 the first two experiments have run successfully which really exhibit the features of homogeneous dynamos. Such experiments are not only desirable as demonstrations of the dynamo principle. They provide us with findings which can hardly be obtained otherwise, e.g., concerning the highly nonlinear interaction of magnetic fields and fluid motions in parameter ranges in which numerical simulations are very difficult. Moreover the interplay between theoretical predictions and experimental results is a strong stimulus to proceed to a deeper understanding of the dynamo phenomenon.
A few basic ideas of dynamo theory will be reviewed, and a survey will be given on the attempts to study dynamo action in conducting fluids experimentally. Some problems will be addressed for which further experimental investigations are of high interest.
Generation and self-excitation of the magnetic field in technical devices
I.M. Kirko and G.E. Kirko
Institute of physical problems of technology "Magnet", Perm, Russia
From positions of modern representations about generation and self-excitation of a magnetic field the experimental results published earlier on generation of a magnetic field in a fast breeder reactor BN-600 are described and discussed. Studying of character of change of a magnetic field around the vessel BN-600 has allowed to break all observed effects into two groups. The first (heat power being equal to zero) - large-scale skin-effect and amplification of a magnetic field to the centre of the pressure chamber. The second - existence of thermoelectric currents inside the device, increase of amplitude of fluctuations of intensity of a magnetic field in area of the driving wheel of the main circulating pump and self-excitation of a magnetic field in the central part of a nuclear reactor for which, in our opinion, the processes proceeding in the pressure head chamber are responsible. All these effects were observed when the reactor was on capacity. Calculation of thermoelectric streams is resulted on the basis of the electric equivalent circuit for a in liquid-metal fast breeder reactors BN-600, BN-1600 and the French reactor "Super-Phenix". Calculations for BN-600 have received experimental and theoretical acknowledgement It allows with a known degree of trust concerns to the results received for BN-1600 and "Super Phoenix", and to state a hypothesis explaining outflow of sodium from a tank of endurance of nuclear fuel on a reactor "Super Phoenix". The leak has been found out in welded seams of a tank of the basic case on an external surface of a lateral wall. The subsequent research has revealed also presence of a crack in width some millimetres in three meters from the bottom of a tank, and also additional cracks in a zone of the welded plates for fastening cooling pipes[1]. In our opinion, these phenomena can be explained by the increased corrosion in the field of the welded seams, caused by the big thermoelectric currents and non-uniform distribution of induction currents which occurrence is caused by MHD-processes inside a reactor.
The phenomenon of generation of a magnetic field grows with an output of a reactor by capacity. For the description of influence of gradients of temperatures in a combination to movement of liquid metal are entered in addition to usual two more dimensionless parameters: . Which on physical sense represents the relation of density of energy of a magnetic field of thermoelectric currents to density of kinetic energy of swirl motion in the pressure chamber, and a simplex , which allows to compare hydrodynamical features of structurally similar reactors. Here T - a difference of temperatures on an input and an output from an reactor core, R0 - radius of the pressure chamber, 0 - a magnetic constant, and - conductivity and density of liquid sodium, T– the thermoelectric coefficient of the conducting sodium-steel medium, -factor of alpha-effect, vхар - characteristic speed of liquid metal in the pressure chamber.
Experiment on research of processes in liquid-metal fast breeder reactors is offered at values Lu>4 in laboratory conditions.
In isothermal conditions excitation of a magnetic field in reactor BN-600 was not observed, distortion of a magnetic field of the Earth around of a reactor however is revealed at current of liquid metal inside a reactor that can serve as an original control method of measurements in a reactor by the decision of a inverse problem: on distortion of a magnetic field to calculate a field of flow in a reactor. Subsequently the similar phenomenon was found out on a blast furnace №6 in Magnitogorsk metallurgical combine by professor Fedulov J.V. (the private message).
Processes of generation of a magnetic field in powerful aluminium reduction cells with electromagnetic management and the electromagnetic phenomena in plasmas jet are discussed. The jet turns out at burning rockets at the special stand. The external magnetic field is created by the special solenoid. Electromagnetic processes are considered and at the expiration of a jet in conditions of a magnetic field of the Earth.
Shearing and embedding box simulations of the MRI
A. Brandenburg et al.
Nordita, Copenhagen, Denmark
Two different computational approaches to the magnetorotational instability (MRI) are pursued: the shearing box approach which is suited for local simulations and the embedding box approach whereby a Taylor Couette flow is embedded in a box so that numerical problems with the coordinate singularity are avoided. New shearing box simulations are presented and differences between regular and hyperviscosity are discussed. Preliminary simulations of spherical nonlinear Taylor Couette flow in an embedding box are presented and the effects of an axial field on the background flow are studied.
Proposal for a Taylor-Dean experimentto investigate the magnetorotational instability
G. Gerbeth, F. Stefani
Forschungszentrum Rossendorf, Dresden, Germany
The magnetorotational instability (MRI) is one of the most promising candidates to explain why accretion disks, which exhibit a Keplerian flow profile and should therefore be hydrodynamically stable, allow for a rate of angular transport which cannot be attributed to the molecular viscosity of the disk. Like the dynamo effect, MRI occurs only at large magnetic Reynolds numbers, making its laboratory investigation rather expensive. Recently, there are strong activities to study MRI in a liquid metal Taylor-Couette flow, and it might be that MRI has already been found in a spherical Couette flow of liquid sodium. We propose an alternative experimental configuration which is based on the Taylor-Dean flow. This flow is a combination of the usual cylindrical Couette flow and an additional Dean flow which is driven by an azimuthal force. This force can be realized in the form of an externally applied pressure gradient or, more elegantly, by a Lorentz force due to a radial current and an axial magnetic field. Our main idea is that, for a well adjusted ratio of Dean flow to Taylor-Couette flow, one gets an angular velocity that is decreasing with the radius and an angular momentum that is increasing with the radius, hence a situation that is prone to the study of MRI. Our main focus is on a particular configuration in which the outer and inner cylinders rotate at the same angular velocity. Evidently, this would simplify the mechanical part of the experiment dramatically. We find that, for sufficiently small values of the ratio of inner to outer radius, such an experiment seems indeed feasible.
Stability of MHD elliptical flow
K.A. Mizerski
WarsawUniversity, Institute of Geophysics,Warsaw,Poland
The three-dimensional instability of elliptical flow, meaning a two-dimensional elliptical vortex was first numerically studied by Pierrehumbert (Phys. Rev. Lett. 1986) and theoretically by B. J. Bayly (Phys. Rev. Lett. 1986). He presented analysis of three-dimensional perturbation acting on the elliptical flow and obtained the groth rates as a result of a matrix Floquet problem which agreed with the Pierrehumbert's results. I extend this analysis to an analogical flow of a conducting fluid in a presence of a magnetic field alinged with the axis of the vortex and I study the influence of the magnetic field on the stability of this system.
Hypersonic flow over body in magnetic fields of different configuration: dissipative magnetic hydrodynamics
A.P. Likhachev, E.V. Gubanov, and S.A. Medin
Institute for High Energy Densities,
Associated Institute for High Temperatures,
RussianAcademy of Sciences,
Moscow, Russia
The airflow past the body with embedded linear magnetic dipole in the presence of uniform external magnetic field is numerically studied. The body represents a long bar moving in atmosphere with constant hypersonic velocity. The velocity and dipole magnetic moment vectors are normal to the body longitudinal axis. The mathematical model of the process considered is constructed in the following assumptions. The airflow is described in the model of the perfect inviscid compressible gas, equilibrium ionized in its passage through bow shock. The low-frequency (MHD) approximation with neglect of the Hall effect is used for simulation of the electrodynamic phenomena. The total magnetic field B is defined as superposition of induced (Bi), external (Be=10-4T) and dipole (Bd) magnetic fields - B=Bi+Be+Bd.
Under these conditions the problem can be formulated as two-dimensional in the plane normal to the body longitudinal axis. The solution of the gasdynamic part of equations is based on the well-known Godunov's method. To solve the equation of magnetic induction the numerical algorithm with non-uniform pattern of convective term approximation has been elaborated. The problem is considered in a coordinate system associated with the body. Pressure and density in the incoming flow are close to the Earth atmosphere parameters at an altitude of ~65 km: pl=10 Pà, l=1,765 10-4 kg/m3. The incoming flow velocity u1 is assigned equal to 7 103 m/s. Specific heat ratio =1.13 and gas constant R=458 j/(kg Ê) have been chosen to provide minimum error of parameter determination in shock-compressed plasma behind the bow shock. The body has the square cross-section with side of 4 m. The distance between wires of magnetic dipole is equal to 2 m.
The numerical analysis of the problem considered has been carried out for parallel and normal orientations of the dipole magnetic moment vector in respect of the incoming flow direction. In both versions of calculations MHD effects lead to the increase of the distance between bow shock and the body and to the suppression of gasdynamic vortexes in the body bottom region. The solutions obtained are characterized by the appearance of the X points in which the magnetic field is equal to zero and the magnetic reconnection occurs. A position and a number of the X points depend of vector orientation aforementioned. The transformation of magnetic energy in the heat and kinetic energy of the plasma leads to the generation of the MHD jets. In the case of the normal vector orientation pressure values behind the bow shock and on the upstream body wall are substantially less that in clearly gasdynamic flow. The results of the given research may be useful to develop the MHD method of flow control for perspective
hypersonic aircraft and to understand some aspects of the interaction of the solar wind with the Earth magnetosphere.
Measuring magnetic helicities in the interstellar medium
A. Shukurov et al.
School of Mathematics and Statistics, University of Newcastle, Newcastle, UK
The helicity of the magnetic field has been identified as key quantity that controls the nonlinear behaviour of the astrophysical magnetic fields subject to dynamo action. We suggest a method to determine the current helicity of the interstellar magnetic field from observations of synchrotron emission and Faraday rotation of supernova remnants. In many remnants, both observables are dominated by a dense shell of compressed interstellar gas, where the line-of sight electric current density and magnetic field are amplified by the compression. The available sensitivity and resolution of radio polarization observations appear to be sufficient to deduce the distributions of the line-of-sight component of the electric current and magnetic field across a number of supernova remnants. When applied to remnants of a size less than 100 pc, this method can provide accurate estimates of the current helicity at various positions in both hemispheres of the Milky Way. This is the first method to estimate the magnetic helicity in the interstellar medium.
Non-axisymmetric solar and stellar
dynamo waves
K. M. Kuzanyan
IZMIRAN, Moscow, Russia
For a simplified one-dimensional modelfor linear 2-dynamo waves in a thin turbulent, differentiallyrotating convective stellar shell.We construct an asymptotic solution using the small aspect ratio of theshell as extension of previous asymptotic WKB studies of dynamo waves.These effects are measured by the magnetic Reynolds numbers R and R.The dynamo wave, which propagates towards the equator,is localised at some mid-latitudes under a Gaussian envelope.We also include the influence of a latitudinaldependent zonal flow and consider the possibility of non-axisymmetric dynamowaves with in general non-zero azimuthal wave number m.We find that the critical dynamo numberDc=R R isminimised by axisymmetric modes in the -limit(R 0). On the other hand, when R0 thereexist a band of wave numbers 0<m<m†,for which thenon-axisymmetric modes have a smaller Dc than in the axisymmetric case.This happens because the wind-up of the non-axisymmetric structurescan be compensated by phase mixing inherent to the
2-dynamo.Therefore, the dynamo wave not only propagates equatorwards but also westwardsrelative to the local angular velocity.Since m† 0 as R 0, the existence of suchmodes, which requires |m†|1, imposes an upper limit onthe size ofthe latitudinal angular velocity gradient. We discuss astrophysical relevance of our findings.
Butterfly diagrams for active late-type stars
M.M. Katsova1 and M.A. Livshits2
1SternbergState Astronomical Institute, MoscowState
University
2Institute of Terrestrial Magnetism, Ionosphere and Radio Wave
Propagation of RussianAcademy of Sciences,
Moscow, Russia
Contrary to results of different techniques of imaging of stellar surfaces where a role of active longitudes in spot distribution is dominated, we argue that latitudinal spot distribution and its temporal variations effect on features of stellar variability. The analysis of long-term photometric variability carried out in the frameworks of the zonal spottedness models by Alekseev and Gershberg (1997) allowed us to realize plotting of the butterfly diagrams for strongly spotted stars and to reveal a drift of spots toward the equator when the total spot area grows. We discuss also how to obtain the butterfly diagrams for late-type stars from differential rotation derived both directly from long-term brightness variations (using Wavelet, Fourier or other methods of spectral-temporal analysis) and from migration of active longitudes as it is proposed by Berdyugina (2004).
Anharmonicity of stellar cycles:
a wavelet quantification
E.Popova1, S.Baliunas2, P.Frick1, D.Moss3, D.Sokoloff4, W.Soon2
1 Institute of Continuous Media Mechanics, Perm, Russia
2 Harvard-SmithsonianCenter for Astrophysics, Cambridge, USA
3 Mathematics Department Manchester University, Manchester, UK
4 Department of Physics, MoscowStateUniversity, Moscow, Russia
A simple explanation of solar and stellar activity cycles in terms of dynamo theory in a prescribed velocity field (the kinematic dynamo) results in harmonic activity waves with amplitudes that grow exponentially in time. More complicated dynamo models result is anharmonic dynamo waves. The shape of dynamo wave underlying a stellar activity cycle depends on details of dynamo excitation. In particular, deviations from harmonic shape appear to be a fruitful source of information concerning stellar dynamo. The aim of our research is to suggest robustmethods to estimate this anharmonisty from observational data and compare it with the results of dynamo simulations.
Simple scaling theory of intense atmospheric vortices based on a kinetic dynamo concept
M.V. Kurgansky 1,2
1 A.M. Obukhov Institute of Atmospheric Physics
Russian Academy of Sciences, Moscow, Russia
2 Department of Atmospheric and Oceanic Physics
Faculty of Physical and Mathematical Sciences
University of Concepción,Concepción,Chile
Simple scaling arguments, based on a 'kinetic dynamo' model that
uses the double-length scale approach (for electrically non-conducting fluids), are proposed to explain nearly inviscid nature of the airflow in intense atmospheric vortices-in theirs mature, quasi-steady stage-driven by small-scale helical turbulence of convective origin. This dynamo model accounts not only for the kinetic alpha effect, which explains the large-scale vortex flow generation, but also for the backward damping action of the mean rotational flow on the small-scale turbulence. The latter effect is analogous to the Lorentz force damping action on small-scale helical fluid motions in the magnetohydrodynamical problem, taken in the limit of low magnetic Reynolds number values. The scaling theory uses, as its essential ingredient, a 'saturation principle' for the helicity bulk density of the turbulent flow component, which is driven by the buoyant convection, and predicts the equality of the vorticity magnitude for the main vortex and small-scale flow component. The latter property is reminiscent of the two-dimensional turbulence and in our case serves a manifestation of the Proudman-Taylor theorem. In the considered kinetic dynamo model, the scale separation between large, L, and small, l, flow scales is estimated, and this estimate is compared to that based on complementary thermodynamical arguments, have been applied to the main vortex flow. Large values of the resulting ratio, L/l > 1, explain nearly inviscid nature and longevity of intense atmospheric vortices, where the Kolmogorov cascade is inhibited-due to the fast main-flow-rotation-and constrained from above by the l-scale. An attempt is also presented to outline basic similarities and differences between kinetic dynamos, on one hand, and conventional dynamos in the magnetohydrodynamics, on the other hand. In our opinion, this inter-comparison may also contribute to better understanding the reasons for success of the dynamo models in the magnetohydrodynamics.